Notably, the device itself is buggy. With Windows 7 default drivers, it claims only 7.1 channel support. No 5.1, nor even stereo. On top of that, it's totally silent. It takes their proprietary driver to get it working reasonably.

With Linux, the same 7.1-only limitation applies... but when hotplugged, PulseAudio sees it as only stereo INPUT.
If I kill pulseaudio, it defaults to muted, but works when I unmute it... until I change output type away from "analog speakers".
Then it drops the slider to zero and won't bring it back.

Now I only see one Speaker slider, instead of the two I saw before... but it has likely totally bogus dB values (between +0.0 and +0.14).

There are a number of reports on this bugtracker related to this buggy hardware (CM106).